Subgroups — C₂²×C₄×#10621873 #25960607

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10621873	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10621873	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#13063257	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13063250	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13063247	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
11	C₂³×C₄×D₄₃	—	2	1	no	—
12	C₂²×#10621873	C₄	1	16	yes	direct product factor
13	C₂²×#10621873	C₂²	1	12	yes	—
14	C₂×C₄×Dic₈₆	—	2	6	no	—
15	C₂×C₄×Dic₈₆	C₂²	1	12	yes	complemented
16	C₂×C₄×D₁₇₂	—	2	6	no	—
17	C₂×C₄×D₁₇₂	C₂²	1	12	yes	—
18	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₄₃⋊C₄	—	2	1	no	—
21	C₂²×(C₂×D₄₃)⋊C₄	—	2	1	no	—
22	C₂²×C₄×Dic₄₃	—	2	1	no	—
23	C₄×#10621873	C₂²	1	64	yes	direct product factor
24	C₂×#13063257	C₂²	1	12	yes	complemented
25	C₂×#13063250	C₂²	1	12	yes	complemented
26	C₂×#13063247	C₂²	1	12	yes	—
27	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₃	C₂²	1	12	yes	complemented
31	C₂⁴×D₄₃	—	2	1	no	—
32	C₂²×Dic₈₆	—	2	3	no	—
33	C₂²×Dic₈₆	—	2	4	no	—
34	C₂²×Dic₈₆	C₂×C₄	1	8	yes	complemented
35	C₂²×Dic₈₆	C₂³	1	6	yes	—
36	C₂²×D₁₇₂	—	2	3	no	—
37	C₂²×D₁₇₂	—	2	4	no	—
38	C₂²×D₁₇₂	C₂×C₄	1	8	yes	—
39	C₂²×D₁₇₂	C₂³	1	6	yes	—
40	C₂³×Dic₄₃	—	2	1	no	—
41	C₂³×Dic₄₃	—	2	1	no	—
42	C₂³×Dic₄₃	—	2	1	no	—
43	C₂²×C₄×D₄₃	—	2	12	no	—
44	C₂²×C₄×D₄₃	—	4	8	no	—
45	C₂×#10621873	C₂×C₄	1	96	yes	direct product factor
46	C₂×#10621873	C₂³	1	16	yes	—
47	C₄×Dic₈₆	—	2	24	no	—
48	C₄×Dic₈₆	C₂³	1	16	yes	complemented
49	C₄×D₁₇₂	—	2	24	no	—
50	C₄×D₁₇₂	C₂³	1	16	yes	—
51	C₂×C₄⋊Dic₄₃	—	2	3	no	—
52	C₂×C₄⋊Dic₄₃	—	2	3	no	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
55	C₂×Dic₄₃⋊C₄	—	2	12	no	—
56	C₂×(C₂×D₄₃)⋊C₄	—	2	12	no	—
57	C₂×C₄×Dic₄₃	—	2	12	no	—
58	#13063257	C₂³	1	16	yes	complemented
59	#13063250	C₂³	1	16	yes	complemented
60	#13063247	C₂³	1	16	yes	—
61	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₃	—	2	4	no	—
65	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
66	C₂²×C₈×C₄₃	C₂³	1	6	yes	—
67	C₂²×C₈×C₄₃	C₂³	1	6	yes	—
68	C₂×C₄²×C₄₃	D₄	1	6	yes	—
69	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
70	C₄×C₈×C₄₃	C₂³	1	16	yes	complemented
71	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂³×D₄₃	—	2	8	no	—
73	C₂³×D₄₃	—	2	6	no	—
74	C₂³×D₄₃	—	4	4	no	—
75	C₂³×D₄₃	—	4	4	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	SD₁₆	1	8	yes	complemented
78	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
80	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
81	C₂²×C₄×C₄₃	C₂×D₄	1	6	yes	—
82	C₂²×C₄×C₄₃	#41	1	4	yes	—
83	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
84	C₂²×Dic₄₃	—	2	8	no	—
85	C₂²×Dic₄₃	—	2	6	no	—
86	C₂²×Dic₄₃	—	2	6	no	—
87	C₂²×Dic₄₃	—	2	6	no	—
88	C₂²×Dic₄₃	—	4	4	no	—
89	C₂²×Dic₄₃	—	4	4	no	—
90	C₂×D₁₇₂	—	2	24	no	—
91	C₂×D₁₇₂	—	2	6	no	—
92	C₂×D₁₇₂	—	2	12	no	—
93	C₂×D₁₇₂	C₂²×C₄	1	24	yes	—
94	C₂×D₁₇₂	C₂⁴	1	4	yes	—
95	C₂×C₄×D₄₃	—	2	16	no	—
96	C₂×C₄×D₄₃	—	4	48	no	—
97	C₂×Dic₈₆	—	2	24	no	—
98	C₂×Dic₈₆	—	2	6	no	—
99	C₂×Dic₈₆	—	2	12	no	—
100	C₂×Dic₈₆	C₂²×C₄	1	24	yes	complemented
101	C₂×Dic₈₆	C₂⁴	1	4	yes	—
102	C₂×C₈×C₄₃	—	2	12	no	—
103	C₂×C₈×C₄₃	C₂²×C₄	1	24	yes	complemented
104	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
106	C₄²×C₄₃	C₂×D₄	1	12	yes	—
107	C₄²×C₄₃	C₂⁴	1	4	yes	—
108	(C₂×D₄₃)⋊C₄	—	2	16	no	—
109	C₄⋊Dic₄₃	—	2	6	no	—
110	C₄⋊Dic₄₃	—	2	6	no	—
111	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
112	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
113	Dic₄₃⋊C₄	—	2	16	no	—
114	C₄×Dic₄₃	—	2	16	no	—
115	#10621873	C₂²×C₄	1	64	yes	direct product factor
116	C₂³×C₄₃	C₄×D₄	1	4	yes	—
117	C₂³×C₄₃	C₂×SD₁₆	1	4	yes	—
118	C₂³×C₄₃	#135	1	4	yes	—
119	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
120	C₂²×D₄₃	—	2	24	no	—
121	C₂²×D₄₃	—	2	4	no	—
122	C₂²×D₄₃	—	4	12	no	—
123	C₂²×D₄₃	—	4	12	no	—
124	C₂²×D₄₃	—	4	32	no	—
125	C₂×C₄×C₄₃	—	2	12	no	—
126	C₂×C₄×C₄₃	C₄×D₄	1	12	yes	—
127	C₂×C₄×C₄₃	C₂×SD₁₆	1	24	yes	complemented
128	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
129	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
130	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
131	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
132	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
133	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
134	C₂×Dic₄₃	—	2	24	no	—
135	C₂×Dic₄₃	—	2	4	no	—
136	C₂×Dic₄₃	—	2	4	no	—
137	C₂×Dic₄₃	—	2	4	no	—
138	C₂×Dic₄₃	—	4	12	no	—
139	C₂×Dic₄₃	—	4	12	no	—
140	D₁₇₂	—	2	24	no	—
141	D₁₇₂	—	2	4	no	—
142	D₁₇₂	C₂³×C₄	1	8	yes	—
143	C₄×D₄₃	—	4	32	no	—
144	Dic₈₆	—	2	24	no	—
145	Dic₈₆	—	2	4	no	—
146	Dic₈₆	C₂³×C₄	1	8	yes	complemented
147	C₈×C₄₃	—	2	4	no	—
148	C₈×C₄₃	C₂³×C₄	1	8	yes	complemented
149	C₂²×C₄×SD₁₆	—	43	1	no	maximal, Sylow
150	C₂²×C₄₃	C₄×SD₁₆	1	16	yes	complemented
151	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
152	C₂²×C₄₃	C₂²×SD₁₆	1	6	yes	—
153	C₂²×C₄₃	C₂×#135	1	6	yes	—
154	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
155	C₂×D₄₃	—	2	8	no	—
156	C₂×D₄₃	—	4	48	no	—
157	C₂×D₄₃	—	4	4	no	—
158	C₂×D₄₃	—	4	4	no	—
159	C₄×C₄₃	—	2	4	no	—
160	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
161	C₄×C₄₃	C₂²×SD₁₆	1	8	yes	complemented
162	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
163	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
164	Dic₄₃	—	2	8	no	—
165	Dic₄₃	—	4	4	no	—
166	Dic₄₃	—	4	4	no	—
167	C₂³×SD₁₆	—	43	1	no	—
168	C₂²×C₄×Q₈	—	43	1	no	—
169	C₂²×C₄×D₄	—	43	1	no	—
170	C₂×C₄×SD₁₆	—	43	24	no	—
171	C₂²×#106	—	43	1	no	—
172	C₂²×#103	—	43	1	no	—
173	C₂²×#102	—	43	1	no	—
174	C₂²×C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
175	C₂×C₄₃	C₂×C₄×SD₁₆	1	12	yes	complemented
176	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
177	C₂×C₄₃	C₂³×SD₁₆	1	1	yes	characteristic
178	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
179	D₄₃	—	4	8	no	—
180	C₂³×Q₈	—	43	1	no	—
181	C₂³×D₄	—	43	1	no	—
182	C₂⁴×C₄	—	86	1	no	—
183	C₂²×SD₁₆	—	43	12	no	—
184	C₂²×SD₁₆	—	43	16	no	—
185	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
186	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
187	C₂×C₄×Q₈	—	43	12	no	—
188	C₂×C₄×Q₈	—	86	6	no	—
189	C₂×C₄×D₄	—	43	12	no	—
190	C₂×C₄×D₄	—	86	6	no	—
191	C₂²×C₄⋊C₄	—	43	1	no	—
192	C₂²×C₄⋊C₄	—	43	1	no	—
193	C₂²×C₄⋊C₄	—	86	1	no	—
194	C₂²×C₂²⋊C₄	—	86	1	no	—
195	C₂²×C₄²	—	86	1	no	—
196	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
197	C₄×SD₁₆	—	43	64	no	—
198	C₂×#106	—	43	12	no	—
199	C₂×#103	—	43	12	no	—
200	C₂×#102	—	43	12	no	—
201	C₂×C₄×C₈	C₂×D₄₃	1	12	yes	complemented
202	C₄₃	C₂²×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
203	C₂⁵	—	86	1	no	—
204	C₂²×Q₈	—	43	8	no	—
205	C₂²×Q₈	—	43	6	no	—
206	C₂²×Q₈	—	86	3	no	—
207	C₂²×Q₈	—	86	4	no	—
208	C₂²×D₄	—	43	8	no	—
209	C₂²×D₄	—	43	6	no	—
210	C₂²×D₄	—	86	3	no	—
211	C₂²×D₄	—	86	4	no	—
212	C₂³×C₄	—	86	1	no	—
213	C₂³×C₄	—	86	1	no	—
214	C₂³×C₄	—	86	1	no	—
215	C₂³×C₄	—	86	12	no	—
216	C₂³×C₄	—	172	8	no	—
217	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
218	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
220	C₂×SD₁₆	—	43	96	no	—
221	C₂×SD₁₆	—	43	16	no	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	C₄×D₄₃	1	8	yes	complemented
224	C₂²×C₈	C₂²×D₄₃	1	6	yes	—
225	C₂²×C₈	C₂²×D₄₃	1	6	yes	—
226	C₄×Q₈	—	43	16	no	—
227	C₄×Q₈	—	86	24	no	—
228	C₄×D₄	—	43	16	no	—
229	C₄×D₄	—	86	24	no	—
230	C₂×C₄⋊C₄	—	43	6	no	—
231	C₂×C₄⋊C₄	—	43	6	no	—
232	C₂×C₄⋊C₄	—	86	3	no	—
233	C₂×C₄⋊C₄	—	86	3	no	—
234	C₂×C₄⋊C₄	—	86	12	no	—
235	C₂×C₂²⋊C₄	—	86	12	no	—
236	C₂×C₄²	—	86	12	no	—
237	C₂×C₄²	D₁₇₂	1	6	yes	—
238	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
239	#106	—	43	16	no	—
240	#103	—	43	16	no	—
241	#102	—	43	16	no	—
242	C₄×C₈	C₂²×D₄₃	1	16	yes	complemented
243	C₂⁴	—	86	8	no	—
244	C₂⁴	—	86	6	no	—
245	C₂⁴	—	172	4	no	—
246	C₂⁴	—	172	4	no	—
247	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
248	C₂×Q₈	—	43	24	no	—
249	C₂×Q₈	—	43	4	no	—
250	C₂×Q₈	—	86	24	no	—
251	C₂×Q₈	—	86	6	no	—
252	C₂×Q₈	—	86	12	no	—
253	C₂×D₄	—	43	24	no	—
254	C₂×D₄	—	43	4	no	—
255	C₂×D₄	—	86	24	no	—
256	C₂×D₄	—	86	6	no	—
257	C₂×D₄	—	86	12	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	86	8	no	—
260	C₂²×C₄	—	86	6	no	—
261	C₂²×C₄	—	86	6	no	—
262	C₂²×C₄	—	86	6	no	—
263	C₂²×C₄	—	86	16	no	—
264	C₂²×C₄	—	172	4	no	—
265	C₂²×C₄	—	172	4	no	—
266	C₂²×C₄	—	172	48	no	—
267	C₂²×C₄	#10621873	1	8	yes	direct product factor
268	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
269	C₂²×C₄	C₂×D₁₇₂	1	6	yes	—
270	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
271	C₂²×C₄	C₂×D₁₇₂	1	6	yes	—
272	C₂²×C₄	#10621898	1	4	yes	—
273	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
274	SD₁₆	—	43	64	no	—
275	C₂×C₈	—	2	12	no	—
276	C₂×C₈	C₂×C₄×D₄₃	1	24	yes	complemented
277	C₂×C₈	C₂³×D₄₃	1	4	yes	—
278	C₂×C₈	C₂³×D₄₃	1	4	yes	—
279	C₄⋊C₄	—	43	4	no	—
280	C₄⋊C₄	—	43	4	no	—
281	C₄⋊C₄	—	86	6	no	—
282	C₄⋊C₄	—	86	6	no	—
283	C₄⋊C₄	—	86	16	no	—
284	C₂²⋊C₄	—	86	16	no	—
285	C₄²	—	86	16	no	—
286	C₄²	C₂×D₁₇₂	1	12	yes	—
287	C₄²	C₂³×D₄₃	1	4	yes	—
288	C₂³	—	86	24	no	—
289	C₂³	—	86	4	no	—
290	C₂³	—	172	12	no	—
291	C₂³	—	172	12	no	—
292	C₂³	—	172	32	no	—
293	C₂³	C₄×D₁₇₂	1	4	yes	—
294	C₂³	C₂×#10621873	1	4	yes	—
295	C₂³	#13063347	1	4	yes	—
296	C₂³	C₂²×D₁₇₂	1	3	yes	—
297	Q₈	—	43	8	no	—
298	Q₈	—	86	24	no	—
299	Q₈	—	86	4	no	—
300	D₄	—	43	8	no	—
301	D₄	—	86	24	no	—
302	D₄	—	86	4	no	—
303	C₂×C₄	—	2	12	no	—
304	C₂×C₄	—	86	24	no	—
305	C₂×C₄	—	86	4	no	—
306	C₂×C₄	—	86	4	no	—
307	C₂×C₄	—	86	4	no	—
308	C₂×C₄	—	172	12	no	—
309	C₂×C₄	—	172	12	no	—
310	C₂×C₄	—	172	32	no	—
311	C₂×C₄	C₄×D₁₇₂	1	12	yes	—
312	C₂×C₄	C₂×#10621873	1	24	yes	direct product factor
313	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
314	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
315	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
316	C₂×C₄	C₂²×D₁₇₂	1	4	yes	—
317	C₂×C₄	C₂×#10621898	1	6	yes	—
318	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
319	C₈	—	2	4	no	—
320	C₈	C₂²×C₄×D₄₃	1	8	yes	complemented
321	C₂²	—	86	8	no	—
322	C₂²	—	172	4	no	—
323	C₂²	—	172	4	no	—
324	C₂²	—	172	48	no	—
325	C₂²	C₄×#10621873	1	16	yes	direct product factor
326	C₂²	C₂×C₄×D₁₇₂	1	6	yes	—
327	C₂²	C₂²×#10621873	1	6	yes	—
328	C₂²	C₂×#13063347	1	6	yes	—
329	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	86	8	no	—
332	C₄	—	172	4	no	—
333	C₄	—	172	4	no	—
334	C₄	C₂×C₄×D₁₇₂	1	6	yes	—
335	C₄	C₂²×#10621873	1	8	yes	direct product factor
336	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
337	C₄	C₂²×#10621898	1	1	yes	characteristic
338	C₂	—	172	8	no	—
339	C₂	C₂×C₄×#10621873	1	12	yes	direct product factor
340	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
341	C₂	C₂³×#10621873	1	1	yes	characteristic
342	C₂	C₂²×#13063347	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	D₁₇₂
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂²×C₄×C₈×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂×D₄
prime radical	C₂³×D₁₇₂	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂²×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂²×C₄×SD₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₄×Dic₈₆	C₂	semidirect
4. C₂×C₄×#10621873	C₂	direct (N × H)
5. C₂²×#13063257	C₂	semidirect
6. C₂²×#13063250	C₂	semidirect
8. C₂²×C₄×C₈×C₄₃	C₂	semidirect
12. C₂²×#10621873	C₄	direct (N × H)
15. C₂×C₄×Dic₈₆	C₂²	semidirect
23. C₄×#10621873	C₂²	direct (N × H)
24. C₂×#13063257	C₂²	semidirect
25. C₂×#13063250	C₂²	semidirect
30. C₂×C₄×C₈×C₄₃	C₂²	semidirect
34. C₂²×Dic₈₆	C₂×C₄	semidirect
45. C₂×#10621873	C₂×C₄	direct (N × H)
48. C₄×Dic₈₆	C₂³	semidirect
58. #13063257	C₂³	semidirect
59. #13063250	C₂³	semidirect
65. C₂²×C₈×C₄₃	C₂×C₄	semidirect
70. C₄×C₈×C₄₃	C₂³	semidirect
77. C₂²×C₄×C₄₃	SD₁₆	semidirect
100. C₂×Dic₈₆	C₂²×C₄	semidirect
103. C₂×C₈×C₄₃	C₂²×C₄	semidirect
115. #10621873	C₂²×C₄	direct (N × H)
127. C₂×C₄×C₄₃	C₂×SD₁₆	semidirect
146. Dic₈₆	C₂³×C₄	semidirect
148. C₈×C₄₃	C₂³×C₄	semidirect
150. C₂²×C₄₃	C₄×SD₁₆	semidirect
161. C₄×C₄₃	C₂²×SD₁₆	semidirect
174. C₂²×C₄×C₈	D₄₃	semidirect
175. C₂×C₄₃	C₂×C₄×SD₁₆	semidirect
201. C₂×C₄×C₈	C₂×D₄₃	semidirect
202. C₄₃	C₂²×C₄×SD₁₆	semidirect
223. C₂²×C₈	C₄×D₄₃	semidirect
242. C₄×C₈	C₂²×D₄₃	semidirect
267. C₂²×C₄	#10621873	direct (N × H)
276. C₂×C₈	C₂×C₄×D₄₃	semidirect
312. C₂×C₄	C₂×#10621873	direct (N × H)
320. C₈	C₂²×C₄×D₄₃	semidirect
325. C₂²	C₄×#10621873	direct (N × H)
335. C₄	C₂²×#10621873	direct (N × H)
339. C₂	C₂×C₄×#10621873	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#10621873	2
C₂²×C₄×Dic₈₆	2
C₂²×C₄×D₁₇₂	2
C₂×C₄×#10621873	2
C₂²×#13063257	2
C₂²×#13063250	2
C₂²×#13063247	2
C₂²×C₄×C₈×C₄₃	2
C₂²×C₄×SD₁₆	43

Subgroups — C22×C4×#10621873 #25960607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#10621873 #25960607